Proclus and the Neoplatonic Syllogistic

An investigation of Proclus' logic of the syllogistic and of negations in the Elements of Theology, On the Parmenides, and Platonic Theology. It is shown that Proclus employs interpretations over a linear semantic structure with operators for scalar negations (hypernegation/alpha-intensivum and privative negation). A natural deduction system for scalar negations and the classical syllogistic (as reconstructed by Corcoran and Smiley) is shown to be sound and complete for the non-Boolean linear structures. It is explained how Proclus' syllogistic presupposes converting the tree of genera and species from Plato's diairesis into the Neoplatonic linear hierarchy of Being by use of scalar hyper and privative negations.     

Combining Possibilities and Negations

Combining non-classical (or sub-classical) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of the logic.     

A First Order Nonmonotonic Extension of Constructive Logic

Certain extensions of Nelson's constructive logic N with strong negation have recently become important in arti.cial intelligence and nonmonotonic reasoning, since they yield a logical foundation for answer set programming (ASP). In this paper we look at some extensions of Nelson's .rst-order logic as a basis for de.ning nonmonotonic inference relations that underlie the answer set programming semantics. The extensions we consider are those based on 2-element, here-and-there Kripke frames. In particular, we prove completeness for .rst-order here-and-there logics, and their minimal strong negation extensions, for both constant and varying domains. We choose the constant domain version, which we denote by QN^c₅, as a basis for de.ning a .rst-order nonmonotonic extension called equilibrium logic. We establish several metatheoretic properties of QN^c₅, including Skolem forms and Herbrand theorems and Interpolation, and show that the .rst-oder version of equilibrium logic can be used as a foundation for answer set inference.     

否定加工的机制到底是什么?——否定加工的心理学理论述评

在否定加工研究领域,存在着两大重要而又对立的心理学理论——命题理论和具身理论。命题理论主要有图式+标签模型和否定的模型理论,它们认为否定是一个抽象的逻辑符号,其作用就是向核心命题(肯定论断)的对立面转换;具身理论主要有两步模拟假设与否定的知觉模拟理论,它们认为否定是以时间耗费或空间延展为表征的具身过程。在介绍两种理论的主要观点以及局限性的基础上,对比分析了二者的异同及其理论方法上的不足,最后提出了否定加工的抑制-反刍-再抑制理论。     

直觉主义逻辑中的否定词

该文从直觉主义否定词的特性出发讨论它存在的可能性,同时比较它与ELMQ中强否定词之间的关系,最后讨论了Heyting系统中两个否定性公理的合理性问题。     

Imagination and the imaginary

This paper argues that real imagination depends on the capacity to acknowledge the absence of what is imagined from the world of material actuality. This leads on to a view of symbol formation as the operation of the transcendent function between the opposites of presence and absence. 'The imaginary' is contrasted with this as a defensive misuse of imagination that attempts to deny 'negation' where negation is defined as all those aspects of the world that constitute a check to the omnipotence of fantasy--e.g., absence, loss, difference, otherness etc. Parallels are drawn with theoretical antecedents in analytical psychology and psychoanalysis, with particular attention to papers published in the Journal of Analytical Psychology (JAP) in the 1960s on the relation between active imagination, transference and ego development. A clinical example is given to show the use of the imaginary as a means of warding off the unbearable pain of Oedipal disappointment.